A152223 a(n) = -4*a(n-1) + 6*a(n-2) for n > 1 with a(0) = 1 and a(1) = -6.

1, -6, 30, -156, 804, -4152, 21432, -110640, 571152, -2948448, 15220704, -78573504, 405618240, -2093913984, 10809365376, -55800945408, 288059973888, -1487045568000, 7676542115328, -39628441869312, 204573020169216, -1056062731892736, 5451689048586240

Offset: 0

Author

Philippe Deléham, Nov 29 2008

Keywords

• sign
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,6).

Crossrefs

Cf. A147703.

Programs

Haskell

a152223 n = a152223_list !! n
a152223_list = 1 : -6 : zipWith (-)
   (map (* 6) $ a152223_list) (map (* 4) $ tail a152223_list)
-- Reinhard Zumkeller, Jan 12 2012

Mathematica

LinearRecurrence[{-4, 6}, {1, -6}, 23] (* Bruno Berselli, Jan 12 2012 *)

PARI

Vec((1-2*x)/(1+4*x-6*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012

Formula

G.f.: (1 - 2*x)/(1 + 4*x - 6*x^2).

a(n) = Sum_{k=0..n} A147703(n,k)*(-7)^k.

a(n) = (1/2)*((-2 - sqrt(10))^n + (-2 + sqrt(10))^n) + (1/5)*sqrt(10)*((-2 - sqrt(10))^n - (-2 + sqrt(10))^n). - Bruno Berselli, Jan 12 2012

Extensions

a(17)-a(23) corrected by Charles R Greathouse IV, Jan 12 2012